Geodesic
Partially observed optimal controls of forward-backward doubly stochastic systems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 3, pp. 828-843

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The partially observed optimal control problem is considered for forward-backward doubly stochastic systems with controls entering into the diffusion and the observation. The maximum principle is proven for the partially observable optimal control problems. A probabilistic approach is used, and the adjoint processes are characterized as solutions of related forward-backward doubly stochastic differential equations in finite-dimensional spaces. Then, our theoretical result is applied to study a partially-observed linear-quadratic optimal control problem for a fully coupled forward-backward doubly stochastic system.

DOI : 10.1051/cocv/2012035
Classification : 93E20, 60H10
Keywords: forward-backward doubly stochastic system, partially observed optimal control, maximum principle, adjoint equation 
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     author = {Shi, Yufeng and Zhu, Qingfeng},
     title = {Partially observed optimal controls of forward-backward doubly stochastic systems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {828--843},
     publisher = {EDP-Sciences},
     volume = {19},
     number = {3},
     year = {2013},
     doi = {10.1051/cocv/2012035},
     mrnumber = {3092364},
     zbl = {1269.93138},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012035/}
}
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Shi, Yufeng; Zhu, Qingfeng. Partially observed optimal controls of forward-backward doubly stochastic systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 3, pp. 828-843. doi: 10.1051/cocv/2012035

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